A sequence satisfies an=5an−1−6an−2a_n = 5a_{n-1} - 6a_{n-2}an=5an−1−6an−2 with a0=2,a1=5a_0 = 2, a_1 = 5a0=2,a1=5. Find ana_nan.
an=2n+3na_n = 2^n + 3^nan=2n+3n
an=2⋅2n+3na_n = 2 \cdot 2^n + 3^nan=2⋅2n+3n
an=3⋅2n−2⋅3na_n = 3 \cdot 2^n - 2 \cdot 3^nan=3⋅2n−2⋅3n
an=2n+2⋅3na_n = 2^n + 2 \cdot 3^nan=2n+2⋅3n